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On Lorentz invariance in the quantum theory. II

Published online by Cambridge University Press:  24 October 2008

Arthur Eddington
Arthur Eddington
Affiliation:
Trinity CollegeCambridge
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Extract

1. I appreciate the careful reply which Dirac, Peierls and Pryce (hereafter referred to as DPP) have made to my criticism of the usual theory of the eigen-functions of a hydrogen atom. Their paper will be generally welcomed because there has not, I think, previously been available an authoritative and clear statement of what is assumed and the grounds for assuming it. Their defence, which is partly on lines I had not expected, has required very serious consideration. But the result of making the arguments more explicit is two-fold. The theory is perhaps more self-consistent than it had appeared to be; but on the other hand, the pressing need for amendment becomes too plain to be overlooked. I have endeavoured to show in the last twelve years that this amendment opens out very fertile extensions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 2 , April 1942 , pp. 201 - 209
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

* Symbols in Clarendon type represent operational forms.

* The momenta do not necessarily appear in their true directions in W, because the wave functions are non-algebraic. The momentum due to Ω1 is twisted out of its true direction in this way. But (5) shows that the radial and the ξ4 directions are not distorted by the wave functions; so that the new term, being in the ξ4 direction, will be undistorted.

† But on similar grounds a factor would be expected in the Ω1 term in (5). Evidently the expectation is not to be trusted.

* This is the name used in Relativity Theory of Protons and Electrons. I now prefer to call it the ‘uranoid’.

* I have recently treated the problem at length in Monthly Notices, R. Astr. Soc. 100 (1940), 582.Google Scholar

* Eddington, and Clark, , Proc. Roy. Soc. A, 166 (1938), 469,CrossRefGoogle Scholar equation (4·6).

† The criterion that the fields are the same is that the geodesics coincide. Since the mass is changing, allowance must be made for light-time in fixing the moment when the two fields agree.